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For simplicity, consider a spherical metal shape for shielding cargo/people behind. (The liquid ball is supposed to be between the Sun and the cargo. Not people inside it.)

A problem I see is that it is going to be hard to forge a sphere of metal big enough like that and it is going to be heavy. Would a sphere of metal having air pockets have good (similar) shielding?

Also, when approaching the Sun, the metal may melt.

Would a liquid metal shell perform as well as a solid shell?

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    $\begingroup$ Per the first answer before you changed the question, the radiation shielding of a given material is determined by it's mass not shape. So adding bubbles will make the same thickness of material less effective as radiation shielding until you add enough extra that the mass is same. The material will also be unpredictable as shielding because areas with more voids will be transparent. $\endgroup$ – GremlinWranger Apr 13 at 9:48
  • $\begingroup$ I have heavily edited your question so that the title still matches the text and the current answer. That includes removing the irrelevant pictures and videos. After that, it essentially is still two separate questions. You really have to learn to ask better questions, people here constantly have to edit yours and ask for clarifications. One question at a time, no irrelevant 'fancy' pictures, please. Suggestion: Write your question, do not post it yet, reread it a few hours later for only one reason: Is my question clear enough?. Then, if the answer is yes, post it. $\endgroup$ – Jan Doggen Apr 13 at 10:08
  • $\begingroup$ @GremlinWranger yes, but would the voids also insulate? Less but more? $\endgroup$ – Muze the good Troll. Apr 13 at 18:42
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    $\begingroup$ @Muze, since the question now talks about heat shielding/insulation, yes gas or even better vacuum pockets would reduce heat transfer en.wikipedia.org/wiki/Metal_foam but using a metal for that is worse than starting with something having lower heat transfer properties and foaming that (see standard insulation foam). And if it melts the bubbles will tend to collapse. For ionizing radiation see answers, you want high densities of the required atomic structure depending on what you are shielding against so foam vs solid just changes the volume of the needed shield not the mass. $\endgroup$ – GremlinWranger Apr 14 at 2:31
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The ability of a metal in the liquid state to block radiation is quite similar to the same metal in the solid state.

Ability to block alpha, beta, gamma, and x-ray radiation typically scales with the electron density of the materials. Neutron radiation is more complicated. Metals with high atomic numbers have high electron densities and typically maintain these densities in molten form. The mass density (and the electron density, which is correlates pretty well with the mass density) of molten metals is usually just slightly less than the mass density of the solid form. For example, at atmospheric pressure, the density of solid mercury is reduced by <4% when it melts. The density of solid iron at atmospheric pressure and room temperature is reduced by about 11% at its melting point in the liquid form.

Lead has traditionally been used for shielding because it has a high electron density and is reasonably cheap.

In vacuum, you might have to worry about the rate of evaporation from the molten metal surface, but liquid metals typically have low vapor pressures. A large quantity of molten metal could probably stay liquid for some time, cooling by radiation and evaporation.

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I took it to be a heat shield, like in another, recent question. In that case multiple panels work better than one, and probably foamed metal is better than solid. It will still heat up, even if more slowly, so you'll still need a radiator on the back end. Even the Space Shuttle and ISS, orbiting Earth, needed/need radiators, probably anything manned in space would, too. Anything incandescent is close to an ideal blackbody, which means it absorbs EM radiation well, when you would prefer to reflect it. Whether solid or liquid, glowing hot is worse. That means your heat shield's properties can change with temperature.

Ionizing radiation is more interesting. In particular, for electrons you want LOW atomic masses to reduce secondary x-rays. If you use lead to shield electrons you will need a lot of lead because of the secondary radiation. Plastics work well. Aluminum is actually pretty good.

Neutrons are not impressed by density; they'll go right through lead. For neutrons you want something with both low atomic mass and high scattering cross-section to slow them, and something with a high absorption cross-section to absorb them. Plastics are pretty good because the hydrogen slows and kind of absorbs them, and carbon is a good moderator, but then you get capture gammas. Boron is a workhorse neutron absorber, high absorption cross-section, hundreds of times higher than hydrogen, but also produces gammas. Back it with something dense. The NIST neutron facility uses wax mixed with metal shot. Lithium-6 will absorb neutrons even better than boron, and without gammas, but that's expensive.

Protons and alphas will be stopped by anything that stops the rest of it.

I can't think of a situation where liquids would be preferred, except for specialty applications like liquid scintillators. Not that the nuclear properties would change, but the structural properties are pretty important, too. See WaterMolecule's nice answer for more on liquids.

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